Development of a Graphical Interface for Monte Carlo Simulations of Magnetic Crystals

1
Development of a Graphical Interface for Monte
Carlo Simulations ofMagnetic Crystals

• Thomas Sarvey
• University of Maryland
• William Ratcliff
• NIST
• NCNR

2
The Problem

• want to understand the magnetic properties of
  materials
• Constructing Models and calculating spins is very
  tedious.
• The Goal Create a program to simplify this
  process

3
Why We Care

• Used constantly in everyday life
• Motors
• Transformers
• Hard Drives
• MRAM

4
Magnetism

• Electric Current creates circular magnetic field
  perpendicular to current
• A current loop will create a magnetic dipole

5
Angular Movement of Electrons

• Two kinds of angular motion within atom
• Orbital motion- Classical model is directly
  analogous to a current loop
• Spin Intrinsic quantum mechanical property
  represented as a vector

6
Magnetic Properties of Insulators

• Atoms can end up with net spins.
• Depending on interactions, Spins tend to align in
  certain ways, i.e. Ferromagnetic,
  anti-ferromagnetic, etc.

7
Lattice Structure

• Regular, repeating arrangement of atoms.
• The smallest unique group of atoms is called the
  unit cell.
• Unit cell translates to form whole lattice
• Similarly, the magnetic unit cell, is the
  smallest unique arrangement of atoms and their
  spins.

8
Example

• Crystallographic Unit Cell

• Magnetic Unit Cell

9
Space Groups

• Mathematical symmetry operations i.e..
  rotations, reflections, etc.
• 230 space groups.
• Any crystal lattice can be represented by a space
  group.

10
The Program Atoms

• The user enters the space group and initial
  positions of 1 or more atoms in the lattice.
• Program then creates the crystallographic unit
  cell
• The atoms in the crystallographic unit cell are
  then translated to form the magnetic unit cell.

11
The Program Bonds

• Once the atoms are created, the user can add an
  interaction between any two atoms.
• Along with the connected atoms, the user can
  enter an interaction matrix describing the
  interaction between the spins of the two atoms.
• The bond is then automatically transformed and
  translated throughout the magnetic cell.

12
The Program Continued

• 3D model is displayed.
• Interactions can be interactively added.
• Once atoms and bonds are generated, the ground
  state spin configuration can be found using a
  Monte Carlo Simulation.

13
Ground State

• Ferromagnetic

• Anti-ferromagnetic

14
Simulated Annealing

• Try to minimize energy
• That can become a very difficult calculation for
  large lattices, so we use a Monte Carlo
  Simulation.
• Monte Carlo Simulations use large numbers of
  random configurations to find the best.

15
Simulated Annealing

• Minimize Energy with random spin fluctuations
• E S1JijS2 DxS1x2 DyS1y2 DzS1z2
• Probability of a move to higher Energy
• e ?E/T

16
Example Run
17
Example Run
18
(No Transcript)
19
Translating the Lattice

• Translate Cutoff Cell to reduce finite size
  effects

20
Finding the Ground State

• Magnetization vs. Temperature

• Magnetization vs. Iteration Number

21
Spins at T 10

• Magnetization vs. Iteration Number

22
Spins at T .4

• Magnetization vs. Iteration Number

23
Spins at T .02

• Magnetization vs. Iteration Number

24
Spins at T .005

• Magnetization vs. Iteration Number

25
The Future

• Excitations above the ground state
• Symmetry Constraints

26
And it was the best summer ever